According to The New Cambridge Bibliography of English Literature, Volume 2: 1660-1800, ed. George Watson (Cambridge: Cambridge University Press, 1971), col. 508, "Epigram by Mr Pope, who had cut down three walnut trees" first appeared in Publick Register No. 1 (January 3, 1741), which I haven't seen.

Who is the Lord? Three candidates have been proposed, all Pope's neighbors at Twickenham.

Lord Radnor

Joseph Warton, in his edition of Pope's Works, Vol. V (London: Printed for B. Law et al., 1797), p. 245, wrote, "The Lord is said to be his next neighbour, the then Lord Radnor." This is John Robartes, fourth Earl Radnor (1686-1757).

Lady Ferrers

In Correspondence between Frances, Countess of Hartford, (afterwards Duchess of Somerset,) and Henrietta Louisa, Countess of Pomfret, between the Years 1738 and 1741, 2nd ed., Vol. II (London: Richard Phillips, 1806), p. 186, the poem appears under the heading "Epigram, by Mr. Pope, Who had cut down three walnut trees in a ground belonging to Lady Ferrers (whom he makes a lord). The trees hindered his prospect of her garden." Lady Ferrers was the first Earl Ferrers' second wife and then widow, born Selina Finch (1681-1762).

From Anecdotes by Baptist Noel Turner (1739-1826), ed. Patricia Köster (New York: Garland Publishing, 1982), pp. 59-60 (Anecdote 70), it also appears that the Lord may have been really a Lady. I don't have access to this book, and I can't piece together the entire anecdote from the snippet view in Google Books. All I can reconstruct is this (my ellipses in square brackets indicate gaps):

Mr Pope in a private Company related the following Anecdote of himselfA couple of Trees which grew upon the Grounds of some Lady of Quality obstructed his View, for which reason he sent immediately & without ceremony had them cut down. Being asked why he took so extraordinary a step, "Because says he, I was perfectly sure if I had desired leave it would not have been granted me & as I would not for five hundred Pound have had them remain where they were I thought it the best way to cut them down which would effectualy prevent their hurting my Prospect for the future, & was very ready to pay any damages a Jury would award. However says he I came off [....] Civility & good nature yet it doubtless flatter'd that Vanity the Bard himself avows

YesI am proudI must be proudto see Men not afraid of God afraid of me!

Turner's note: Mrs Cantrell [anec. 13] however who told it me some years ago has just circumstantially repeated it (Nov l780) & insists she heard Mr Pope tell it at Gyles [anec. 74] the booksellers just as here relatedIt is possible then that this may be the truth, & and he might chuse to vary a little in an Epigram he himself wrote upon it something about

Pope stark mad of gardens Cut down three trees in value scarce three farthings [....]

The incident which evoked this epigram is described, curiously enough, by Samuel Richardson. A copy of the lines, made by Richardson, is included in a section of one of the manuscript volumes of his correspondence, preserved at the Victoria and Albert Museum, South Kensington.5 Above the epigram Richardson wrote: "Mr. Pope's servant having lopt6 two or three of My Ld Dysert's Trees; occasioned his master's writing the following lines."

5 Forster MSS., 48 E 10.6 Richardson originally wrote "cut down" in place of "lopt."

This is Lionel Tollemache, fourth Earl Dysart (1708-1770).

Any reader who could send me images of Anecdotes by Baptist Noel Turner (1739-1826), ed. Patricia Köster (New York: Garland Publishing, 1982), pp. 59-60, would do me a great service. The closest public library with a copy of this book is over a hundred miles from where I live.

I asked a friend, owner of an extensive personal library, if he had a copy, and he replied:

Ah, yes, the Reverend Turner's 'Anecdotes'  so runs my mundane bookman's fantasy  turret two in the West Wing, requiring a leisurely stroll down oak-panelled corridors, past the Portland vase, marble busts of ancestors and sundry Old Masters, up a spiral staircase and then ladder to reach the upper shelves of bay D. Do I trust the footman or should I go myself?

No, sorry. 'Anecdotes' is out of my reach.

Update: A kind reader has volunteered to send me a copy of the pages from Turner's Anecdotes.